Depth-averaged models for dry granular flows

Constructing multiple barriers along the predicted flow paths has been recognised as an effective engineering measure to intercept large volumes of debris flows. In the field, barriers usually have a basal clearance, which is an opening between the channel bed and the base of the barrier, to allow small discharges pass through the barrier and prevent the accumulation of stream loads. However, the current design of basal clearance is still based on an empirical criterion. The objectives of this research are to investigate the effects of basal clearance on the interaction between debris flow and multiple rigid barriers and to propose and verify a new analytical framework for flow impact on multiple rigid barriers with basal clearance. Findings from this study can serve to improve the current design guidelines on multiple-barrier system. The newly proposed analytical framework consists of an impact equation for barrier with a basal clearance, discharge equations to estimate flow properties of the basal discharge and a landing equation to estimate the flow properties after flow lands on the basal discharge. To verify the proposed framework, physical and numerical modelling were adopted. A series of dry granular flow tests has been carried out with a 5-m flume model to investigate the fundamental impact behaviour of idealised uniform particles on a rigid barrier with basal clearance. A discrete element model was calibrated by the physical tests and a series of numerical parametric studies has been conducted with varying barrier heights and barrier spacing. Furthermore, due to scale dependent nature of debris flow, a 28-m flume facility has been newly developed to investigate the impact dynamics of debris flow on dual rigid barriers with basal clearance. It is found that basal clearance can be designed to optimise barrier size and minimise maintenance work for a multiple-barrier system. Basal clearance with a ratio between clearance height and flow depth, H<sub>c</sub>/h<sub>i</sub>, ranging from 0.5 to 1.0 with Fr = 7 can reduce the impact force and runup height of two-phase debris flow by up to 55% and 43%, respectively. The effectiveness of basal clearance on mitigating impact can be characterised by Friction number, N<sub>fric</sub>, of the flow. A larger N<sub>fric</sub> represents a higher shear resistance among particles that would resist the flow to be discharged and lead the flow tend to be redirected to parallel to the barrier. N<sub>fric</sub> of dry granular flow that is by up to 55 times higher than the two-phase flow leads the basal clearance about 30% less effective on reducing the impact force and runup height of dry granular flow. Characteristic particle size, d<sub>max</sub> that represents the largest particle of the debris material, is found capable of determining the occurrence of jamming at the basal clearance. Basal clearance height H<sub>c</sub>/d<sub>max</sub> ≤ 2.0 and H<sub>c</sub>/d<sub>max</sub> ≥ 3.0 may lead and not lead jamming at the clearance, respectively, and could be adopted for a barrier to regulate debris flow without losing barrier retention and without retaining any debris, respectively. The proposed impact equation can well estimate both dry granular flow and debris flow impact on a rigid barrier with a basal clearance. The proposed landing equation can provide an upper bound for flow depth and velocity near the landing location. However, with an increasing flow distance, the decrease of downstream flow depth may lead that only the discharge equations are needed to estimate the flow properties.

The endodermal location of 'germinal plasm'-bearing cells (GPBCs) and the ultrastructure of the 'germinal plasm' were studied in Xenopus laevis embryos at gastrula, neurula, tailbud and younger tadpole stages. Primordial germ cells (PGCs) of feeding tadpoles were also observed ultrastructurally. GPBCs were found in the inner endoderm and in the yolk plug region at the late gastrula stage, in the middle and in the dorsal part of the endoderm cell mass at the late neurula and late tailbud stages, respectively. At the younger tadpole stage they were observed in the uppermost dorsal part of the endoderm. Germinal granules were always present in GPBCs at all stages examined but were not found in PGCs of feeding tadpoles. Irregularly shaped-stringlike bodies (ISBs) which seemed to have changed from germinal granules were first noticed in GPBCs at the late neurula stage, and were still present in PGCs of tadpoles, while 'granular materials' were not seen in GPBCs until the feeding tadpole stages. These facts and ultrastructural similarities shared by these organelles lead us to conclude that the change of the germinal granule through ISB, to the 'granular material' takes place during the differentiation of GPBCs into PGCs.

On energy transfer and dissipation of intruder impacting granular materials based on discrete element simulations

Granular materials are extensively used throughout many industries. In countries like Australia and South Africa, national economies are critically dependent on the agricultural and mining industries, and it is important to understand bulk material behaviour in order to handle these materials properly. There are many diverse approaches to modelling granular materials. In this thesis, the Coulomb-Mohr continuum mechanical theory of granular materials is utilised, and some exact analytical solutions are presented for both stress and velocity fields. These solutions are formally valid provided sin φ = 1, where φ is the angle of internal friction, and they provide limiting solutions for so called highly frictional granular materials, for which sin φ ≈ 1. The solutions so obtained are exploited for three real industrial granular problems, namely gravity flow from converging hoppers, the stress distribution in stockpiles and finally, the stress distribution within rat-holes. The flow of granular materials, in the presence of gravity, through a converging hopper is an important problem that occurs in many industrial processes. Here, for highly frictional granular materials for both wedge and conical hopper flows, exact analytical solutions are obtained to determine the stress and velocity fields within the neighborhood of the hopper outlet. For the same problem, these exact solutions are exploited as the leading order terms in a regular perturbation series, where the correction terms are of order 1− sin φ. In this way, approximate analytical solutions are obtained that can be used to describe the behaviour of more realistic granular materials. The practice of storing granular materials in stockpiles occurs throughout the ii world in many industrial situations. In this thesis, exact solutions for highly frictional granular materials are used for the determination of the stress distributions within two-dimensional and axially symmetric stockpiles. Stockpile profiles considered here include the standard wedge and cone, as well as two-dimensional parabolic and axially symmetric cubic curved shaped stockpiles. We emphasise that curved stockpiles have not previously been considered in the literature. Our model assumes that the stockpile is composed of two regions, namely an inner rigid region and an outer yield region. The exact solution applies in the outer yield region, which is then extended continuously into the inner rigid region. A rat-hole is the general term used to describe those stable cavities, which frequently occur in storage hoppers and stockpiles, whose formation prevents further material falling through the outlet. In this thesis, we present exact solutions for both two-dimensional and axially symmetric rat-holes, where it is assumed that the highly frictional granular material has flowed through a central outlet, until the point is reached when there is no further flow of material. The remaining material is assumed to be in limiting equilibrium, that is static but on the point of yield. In both two dimensions and axial symmetry, two types of rat-holes are studied. The first type has a sloping upper surface of infinite extent, where the material is resting on a sloping rigid base containing an infinitesimal central outlet. The second type has a curved upper surface, where the material is resting between vertical walls and a horizontal rigid plane containing an infinitesimal central outlet. Again, we emphasise that neither of these rat-hole problems have previously been investigated in the literature.

This paper deals with the mechanical behaviour, especially the permanent deformation and resilient deformation of an unbound granular material (UGM) from Bréfauchet quarry which is used as base layer material in low traffic pavements for full-scale tests at IFSTTAR in France. Medium-scale repeated load triaxial tests (RLTT) are carried out at different water contents and the results show that both permanent and resilient deformations increase with water content. Besides, two techniques of fixing the sensors in materials with large particles for RLTTs are proposed and compared with each other. The results suggest that the tube method is more suitable for the UGM for an accurate measurement and a good adaptability is obtained during the RLTT. Based on the test results of UGM Bréfauchet, the modelling work is performed with improved models used previously for a sandy material. It appears that both the permanent and resilient behaviours of different unbound granular materials can be well captured by the proposed equations considering the effects of water content and anisotropy. This study is helpful to understand the evolution of permanent and resilient deformation in different granular layers, especially for the base layer, in low traffic pavements. The verified models can be used for other similar granular materials and this will lead to reducing the number of tests required to predict the deformation behaviour of granular materials.

Geophysical granular flows, like avalanches and debris flows, are hazardous phenomena for infrastructures and human activities. The complex dynamics of granular systems, involved in these phenomena, poses important challenges to their reliable mathematical modelling. In this context, laboratory investigations on granular flows and non-invasive optical measuring methods are irreplaceable tools for getting a deeper insight into the granular dynamics, as they provide useful information for model calibration and validation. Frictional and collisional momentum flux exchanges coexist in dense granular flows. These resistance mechanisms and their complex interplay with the boundary conditions generate non-negligible fluxes of translational and fluctuation energies along the flow domain, which also influence the kinematics of the free surface. In this work we study steady granular flows in a chute geometry over a fixed bed, specifically focusing on the spatial fluctuations of the free surface. Several tests have been carried out by systematically varying the mass flow rate, the chute inclination and the basal roughness. The experimental apparatus, consisting of a narrow Plexiglas flume, is equipped with a load cell to measure the mass flow rate and a high-speed camera to get non-invasive optical measurements of the free surface fluctuations. A harmonic analysis, employing the Welch method, is performed on a time-series signal obtained from suitably binarized digital images of the free surface fluctuations, recorded at a sampling frequency of 1 kHz. Subsequently, the power spectral densities and the power content of different frequency intervals are analysed. Meaningful correlations are observed between these power components and other relevant measurements, such as the mass flow rates and the flow depths. These preliminary results may be useful for a better understanding of the momentum exchange mechanisms in granular flows and the related fluctuation energy fluxes.

Multiscale modeling and characterization of coupled damage-healing-plasticity for granular materials in concurrent computational homogenization approach

Skins with asymmetric kirigami scales and soft spikes are integrated to the surface of a base self‐burrowing robot, which consists of a soft one‐segment extending actuator. Friction anisotropy is observed at the interfaces between the burrowing robots and different granular materials. Its effects on the pulling resistance and burrowing characteristics are studied. The results demonstrate that the development of friction and friction anisotropy is affected by the characteristics of the granular material, the asymmetric skins, and the relative size of the asymmetric features to the granular particles. Robots with scales or spikes aligned along the upward direction burrow faster than those aligned against the upward direction, especially in relatively coarser granular materials. Particle image velocimetry analysis on the particle displacement fields around the actuator reveals the complexity of dry granular material interactions with soft robots, implying that aligned scales or spikes can impact the distribution of friction preferentially, opening up many possibilities for thoughtful material and geometry‐based manipulation of friction in the design and optimization of future soft burrowing robots for more versatile locomotion capabilities.

Granular material under the action of gravity flows down an incline tube or plane. This paper presents a phenomenon in which a granular material climbs along a vertically vibrating tube that is partially inserted in a granular silo. In this scenario the final climbing height increases with increasing vibration strength and tube insertion depth. However, the climbing velocity of the granular material does not monotonically increase with the climbing height. A transition height, at which the granular material has the highest climbing velocity, also exists. When the tube vibrates, the force between the tube and the particles varies periodically, thus inducing the directional climbing of particles. By analyzing the forces on the particles, we present a model that is qualitatively consistent with the experimental results.

Heat transfer to flowing granular material

Debris flow is a very common and destructive natural hazard in mountainous regions. Pore water pressure is the major triggering factor in the initiation of debris flow. Excessive pore water pressure is also observed during the runout and deposition of debris flow. Debris materials are normally treated as solid particle–viscous fluid mixture in the constitutive modeling. A suitable constitutive model which can capture the solid-like and fluid-like behavior of solid–fluid mixture should have the capability to describe the developing of pore water pressure (or effective stresses) in the initiation stage and determine the residual effective stresses exactly. In this paper, a constitutive model of debris materials is developed based on a framework where a static portion for the frictional behavior and a dynamic portion for the viscous behavior are combined. The frictional behavior is described by a hypoplastic model with critical state for granular materials. The model performance is demonstrated by simulating undrained simple shear tests of saturated sand, which are particularly relevant for the initiation of debris flows. The partial and full liquefaction of saturated granular material under undrained condition is reproduced by the hypoplastic model. The viscous behavior is described by the tensor form of a modified Bagnold’s theory for solid–fluid suspension, in which the drag force of the interstitial fluid and the particle collisions are considered. The complete model by combining the static and dynamic parts is used to simulate two annular shear tests. The predicted residual strength in the quasi-static stage combined with the stresses in the flowing stage agrees well with the experimental data. The non-quadratic dependence between the stresses and the shear rate in the slow shear stage for the relatively dense specimens is captured.

The discrete-element method (DEM) has gained popularity for developing a qualitative understanding of soil behaviour under a critical state soil mechanics (CSSM) framework. Most studies with a three-dimensional assembly of particles have used spheres as representative granular material to reduce computational demands. However, most granular materials – for example, sands – are not rounded, but possess features of angularity. Therefore, ellipsoid and cluster particles with different degrees of eccentricity were used in this study to evaluate the effect of the particle shape on the drained and undrained triaxial loading behaviour after isotropic and K0 consolidation. The particle numerical properties and grain size distributions were kept the same for all specimens, irrespective of particle shape. The critical state data points for spheres and ellipsoids plotted on almost the same critical state line (CSL) in e–log(p′) space, whereas the CSLs of clusters plotted above them. Additionally, M lines shifted downward with increasing sphericity. It was also found that the stress ratio at the triggering of static liquefaction (ηIS = q/p′) in ηIS–ψ space was affected by particle shape and consolidation path. The dilatancy (d = dεvp/dεqp) was also affected by particle shape. It was found that dilatancy parameters for the SANISAND constitutive model are affected by particle shape, which may contribute to an improved understanding of particle shape in constitutive modelling.

Quasi-static and dynamic compaction of granular materials: A strain-activated statistical compaction model and its evaluation

Granular materials forming part of embankments, foundations and pavement structures are subjected to both static and dynamic loads. As a result, total or partial particle breakage occurs. Particle breakage causes settlements and a reduction in hydraulic conductivity (Fragaszy & Voss, 1986). Previous research has indicated that granular materials undergoing crushing exhibit a non-linear Mohr-Coulomb failure envelope if the envelope is constructed with the peak values of shear resistance. Therefore the angle of shearing resistance decreases as a consequence of particle crushing (Bolton, 1986; Feda, 2002). On the other hand, recent ring shear tests on carbonate sand presented by Coop et al. (2004) showed crushing without loss of residual angle of internal friction. It seems that crushable granular materials experience a reduction in the internal friction angle as a consequence of particle breakage prior to achieving a constant value of residual strength. The main focus of this study is to understand and produce a visualisation of the evolution of crushing in a weak granular material subjected to a direct shear test. The results from direct shear tests conducted on sugar, and a computer simulation using the discrete element method, are presented. (A)

Convective heat transfer to rapidly flowing, granular materials